Pulsating Front Speed-up and Quenching of Reaction by Fast Advection

Details Pulsating Front Speed-up and Quenching of Reaction by Fast Advection Pulsating Front Speed-up and Quenching of Reaction by Fast Advection

2007-04-10

arxiv.org/abs/0704.1164v2

Mathematics

Analysis of PDEs

16pp

Scientific paper

10.1088/0951-7715/20/12/009

We consider reaction-diffusion equations with combustion-type non-linearities in two dimensions and study speed-up of their pulsating fronts by general periodic incompressible flows with a cellular structure. We show that the occurence of front speed-up in the sense $\lim_{A\to\infty} c_*(A)=\infty$, with $A$ the amplitude of the flow and $c_*(A)$ the (minimal) front speed, only depends on the geometry of the flow and not on the reaction function. In particular, front speed-up happens for KPP reactions if and only if it does for ignition reactions. We also show that the flows which achieve this speed-up are precisely those which, when scaled properly, are able to quench any ignition reaction.

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